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  "Package": "matrixdist",
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  "Title": "Statistics for Matrix Distributions",
  "Version": "1.1.9",
  "Date": "2023-08-01",
  "Authors@R": "c(person(\"Martin\", \"Bladt\", email = \"martinbladt@gmail.com\", role = c(\"aut\", \"cre\")),\nperson(\"Jorge\", \"Yslas\", email = \"jorge.yslas1@gmail.com\",\nrole = \"aut\"),\nperson(\"Alaric\", \"Müller\", email = \"muelleralaric@gmail.com\",\nrole = \"ctb\")\n)",
  "Maintainer": "Martin Bladt <martinbladt@gmail.com>",
  "Author": "Martin Bladt [aut, cre], Jorge Yslas [aut], Alaric Müller [ctb]",
  "URL": "https://github.com/martinbladt/matrixdist_1.0",
  "BugReports": "https://github.com/martinbladt/matrixdist_1.0/issues",
  "Description": "Tools for phase-type distributions including the following\nvariants: continuous, discrete, multivariate, in-homogeneous,\nright-censored, and regression. Methods for functional\nevaluation, simulation and estimation using the\nexpectation-maximization (EM) algorithm are provided for all\nmodels. The methods of this package are based on the following\nreferences. Asmussen, S., Nerman, O., & Olsson, M. (1996).\nFitting phase-type distributions via the EM algorithm, Olsson,\nM. (1996). Estimation of phase-type distributions from censored\ndata, Albrecher, H., & Bladt, M. (2019)\n<doi:10.1017/jpr.2019.60>, Albrecher, H., Bladt, M., & Yslas,\nJ. (2022) <doi:10.1111/sjos.12505>, Albrecher, H., Bladt, M.,\nBladt, M., & Yslas, J. (2022)\n<doi:10.1016/j.insmatheco.2022.08.001>, Bladt, M., & Yslas, J.\n(2022) <doi:10.1080/03461238.2022.2097019>, Bladt, M. (2022)\n<doi:10.1017/asb.2021.40>, Bladt, M. (2023)\n<doi:10.1080/10920277.2023.2167833>, Albrecher, H., Bladt, M.,\n& Mueller, A. (2023) <doi:10.1515/demo-2022-0153>, Bladt, M. &\nYslas, J. (2023) <doi:10.1016/j.insmatheco.2023.02.008>.",
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    "sph",
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      "page": "matrixdist-package",
      "title": "Statistics for Matrix Distributions",
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        "matrixdist"
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      "page": "plus-dph-dph-method",
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      "title": "Sum method for phase-type distributions",
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      "title": "Cor method for bivph class",
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      "title": "Cor method for multivariate discrete phase-type distributions",
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      "title": "Cor method for multivariate phase-type distributions",
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      "page": "csph_density",
      "title": "Bivariate phase-type joint density of the common shock type",
      "topics": [
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      "title": "Bivariate phase-type joint density of the common shock type",
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      "title": "Bivariate phase-type joint density of the common shock type",
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      "title": "Bivariate phase-type joint density of the common shock type",
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      "title": "Cumulate matrix",
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      "title": "Default size of the steps in the RK",
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      "page": "dens-bivdph-method",
      "title": "Density method for bivariate discrete phase-type distributions",
      "topics": [
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    {
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      "title": "Density method for multivariate inhomogeneous phase-type distributions",
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      "title": "Density method for multivariate phase-type distributions",
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      "title": "Density method for phase-type distributions",
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      "title": "Constructor function for discrete phase-type distributions",
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      "title": "Pgf of a discrete phase-type distribution",
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      "title": "Discrete phase-type distributions",
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    {
      "page": "dphcdf",
      "title": "Discrete phase-type cdf",
      "topics": [
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    {
      "page": "dphdensity",
      "title": "Discrete phase-type density",
      "topics": [
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    {
      "page": "EM_step_mPH_rc",
      "title": "EM step for the mPH class with right-censoring, for different marginal sub-intensity matrices",
      "topics": [
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      ]
    },
    {
      "page": "embedded_mc",
      "title": "Embedded Markov chain of a sub-intensity matrix",
      "topics": [
        "embedded_mc"
      ]
    },
    {
      "page": "embedded_mc_cs",
      "title": "Embedded Markov chain of a sub-intensity matrix",
      "topics": [
        "embedded_mc_cs"
      ]
    },
    {
      "page": "EMstep_bivdph",
      "title": "EM for discrete bivariate phase-type",
      "topics": [
        "EMstep_bivdph"
      ]
    },
    {
      "page": "EMstep_bivdph_MoE",
      "title": "EM for discrete bivariate phase-type MoE",
      "topics": [
        "EMstep_bivdph_MoE"
      ]
    },
    {
      "page": "EMstep_bivph",
      "title": "EM for bivariate phase-type distributions using Pade for matrix exponential",
      "topics": [
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      ]
    },
    {
      "page": "EMstep_dph",
      "title": "EM for discrete phase-type",
      "topics": [
        "EMstep_dph"
      ]
    },
    {
      "page": "EMstep_dph_MoE",
      "title": "EM for discrete phase-type MoE",
      "topics": [
        "EMstep_dph_MoE"
      ]
    },
    {
      "page": "EMstep_mdph",
      "title": "EM for multivariate discrete phase-type",
      "topics": [
        "EMstep_mdph"
      ]
    },
    {
      "page": "EMstep_mdph_MoE",
      "title": "EM for multivariate discrete phase-type MoE",
      "topics": [
        "EMstep_mdph_MoE"
      ]
    },
    {
      "page": "EMstep_MoE_PADE",
      "title": "EM for PH-MoE",
      "topics": [
        "EMstep_MoE_PADE"
      ]
    },
    {
      "page": "EMstep_PADE",
      "title": "EM for phase-type distributions using Pade approximation for matrix exponential",
      "topics": [
        "EMstep_PADE"
      ]
    },
    {
      "page": "EMstep_RK",
      "title": "EM step for phase-type using Runge-Kutta",
      "topics": [
        "EMstep_RK"
      ]
    },
    {
      "page": "EMstep_UNI",
      "title": "EM for phase-type using uniformization for matrix exponential",
      "topics": [
        "EMstep_UNI"
      ]
    },
    {
      "page": "EMstep_UNI_intervalCensoring",
      "title": "EM for phase-type using uniformization for matrix exponential",
      "topics": [
        "EMstep_UNI_intervalCensoring"
      ]
    },
    {
      "page": "evaluate",
      "title": "New generic for evaluating survival matrix distributions",
      "topics": [
        "evaluate"
      ]
    },
    {
      "page": "evaluate-sph-method",
      "title": "Evaluation method for sph Class",
      "topics": [
        "evaluate,sph-method"
      ]
    },
    {
      "page": "expm_terms",
      "title": "expm terms of phase-type likelihood using uniformization",
      "topics": [
        "expm_terms"
      ]
    },
    {
      "page": "expmat",
      "title": "Matrix exponential",
      "topics": [
        "expmat"
      ]
    },
    {
      "page": "find_n",
      "title": "Find n such that P(N > n) = h with N Poisson distributed",
      "topics": [
        "find_n"
      ]
    },
    {
      "page": "find_weight",
      "title": "Find weight of observations",
      "topics": [
        "find_weight"
      ]
    },
    {
      "page": "Fisher",
      "title": "New generic for obtaining the Fisher information of survival matrix distributions",
      "topics": [
        "Fisher"
      ]
    },
    {
      "page": "Fisher-sph-method",
      "title": "Fisher information method for sph class",
      "topics": [
        "Fisher,sph-method"
      ]
    },
    {
      "page": "fit",
      "title": "New generic for estimating matrix distributions",
      "topics": [
        "fit"
      ]
    },
    {
      "page": "fit_multiple",
      "title": "Fit Multiple Competing Phase-Type Models",
      "topics": [
        "fit_multiple"
      ]
    },
    {
      "page": "fit-bivdph-method",
      "title": "Fit method for bivdph Class",
      "topics": [
        "fit,bivdph-method"
      ]
    },
    {
      "page": "fit-bivph-method",
      "title": "Fit method for bivph Class",
      "topics": [
        "fit,bivph-method"
      ]
    },
    {
      "page": "fit-dph-method",
      "title": "Fit method for dph class",
      "topics": [
        "fit,dph-method"
      ]
    },
    {
      "page": "fit-mdph-method",
      "title": "Fit method for mdph Class",
      "topics": [
        "fit,mdph-method"
      ]
    },
    {
      "page": "fit-mph-method",
      "title": "Fit method for mph Class",
      "topics": [
        "fit,mph-method"
      ]
    },
    {
      "page": "fit-MPHstar-method",
      "title": "Fit method for mph class",
      "topics": [
        "fit,MPHstar-method"
      ]
    },
    {
      "page": "fit-ph-method",
      "title": "Fit method for ph class",
      "topics": [
        "fit,ph-method"
      ]
    },
    {
      "page": "haz",
      "title": "New generic for the hazard rate of matrix distributions",
      "topics": [
        "haz"
      ]
    },
    {
      "page": "haz-ph-method",
      "title": "Hazard rate method for phase-type distributions",
      "topics": [
        "haz,ph-method"
      ]
    },
    {
      "page": "inf_norm",
      "title": "L inf norm of a matrix",
      "topics": [
        "inf_norm"
      ]
    },
    {
      "page": "inhomogeneity_reg",
      "title": "New generic for regression with matrix distributions, when the inhomogeneity parameter is also regressed",
      "topics": [
        "inhomogeneity_reg"
      ]
    },
    {
      "page": "inhomogeneity_reg-ph-method",
      "title": "Regression method for ph Class",
      "topics": [
        "inhomogeneity_reg,ph-method"
      ]
    },
    {
      "page": "initial_state",
      "title": "Initial state of Markov jump process",
      "topics": [
        "initial_state"
      ]
    },
    {
      "page": "iph",
      "title": "Constructor function for inhomogeneous phase-type distributions",
      "topics": [
        "iph"
      ]
    },
    {
      "page": "iph-class",
      "title": "Inhomogeneous phase-type distributions",
      "topics": [
        "iph-class"
      ]
    },
    {
      "page": "laplace",
      "title": "New generic for Laplace transform of matrix distributions",
      "topics": [
        "laplace"
      ]
    },
    {
      "page": "laplace-bivph-method",
      "title": "Laplace method for bivph class",
      "topics": [
        "laplace,bivph-method"
      ]
    },
    {
      "page": "laplace-mph-method",
      "title": "Laplace method for multivariate phase-type distributions",
      "topics": [
        "laplace,mph-method"
      ]
    },
    {
      "page": "laplace-ph-method",
      "title": "Laplace method for phase-type distributions",
      "topics": [
        "laplace,ph-method"
      ]
    },
    {
      "page": "linCom",
      "title": "New generic for linear combinations of multivariate matrix distributions",
      "topics": [
        "linCom"
      ]
    },
    {
      "page": "linCom-bivph-method",
      "title": "Linear combination method for bivariate phase-type distributions",
      "topics": [
        "linCom,bivph-method"
      ]
    },
    {
      "page": "linCom-MPHstar-method",
      "title": "Linear combination method for MPHstar class",
      "topics": [
        "linCom,MPHstar-method"
      ]
    },
    {
      "page": "linear_combination",
      "title": "Computes PH parameters of a linear combination of vector from MPHstar",
      "topics": [
        "linear_combination"
      ]
    },
    {
      "page": "logLik-ph-method",
      "title": "Loglikelihood method for ph class",
      "topics": [
        "logLik,ph-method"
      ]
    },
    {
      "page": "logLikelihood_UNIs_PI",
      "title": "Loglikelihood of PI using uniformization, with customizable observation transformation, automatically handling right-censored or interval-censored data based on the structure of 'rcens'.",
      "topics": [
        "logLikelihood_UNIs_PI"
      ]
    },
    {
      "page": "logLikelihoodbivDPH",
      "title": "Loglikelihood for bivariate discrete phase-type",
      "topics": [
        "logLikelihoodbivDPH"
      ]
    },
    {
      "page": "logLikelihoodbivDPH_MoE",
      "title": "Loglikelihood for bivariate discrete phase-type MoE",
      "topics": [
        "logLikelihoodbivDPH_MoE"
      ]
    },
    {
      "page": "logLikelihoodbivPH",
      "title": "Loglikelihood for Bivariate PH",
      "topics": [
        "logLikelihoodbivPH"
      ]
    },
    {
      "page": "logLikelihoodDPH",
      "title": "Loglikelihood for discrete phase-type",
      "topics": [
        "logLikelihoodDPH"
      ]
    },
    {
      "page": "logLikelihoodDPH_MoE",
      "title": "Loglikelihood for discrete phase-type MoE",
      "topics": [
        "logLikelihoodDPH_MoE"
      ]
    },
    {
      "page": "logLikelihoodmDPH",
      "title": "Loglikelihood for multivariate discrete phase-type",
      "topics": [
        "logLikelihoodmDPH"
      ]
    },
    {
      "page": "logLikelihoodmDPH_MoE",
      "title": "Loglikelihood for multivariate discrete phase-type MoE",
      "topics": [
        "logLikelihoodmDPH_MoE"
      ]
    },
    {
      "page": "logLikelihoodMgev_PADE",
      "title": "Loglikelihood of matrix-GEV using Pade",
      "topics": [
        "logLikelihoodMgev_PADE"
      ]
    },
    {
      "page": "logLikelihoodMgev_RK",
      "title": "Loglikelihood of matrix-GEV using Runge-Kutta",
      "topics": [
        "logLikelihoodMgev_RK"
      ]
    },
    {
      "page": "logLikelihoodMgev_UNI",
      "title": "Loglikelihood of matrix-GEV using uniformization",
      "topics": [
        "logLikelihoodMgev_UNI"
      ]
    },
    {
      "page": "logLikelihoodMgev_UNI_inhom",
      "title": "Loglikelihood of matrix-GEV using uniformization, when the intensity function is regressed on covariate informatino",
      "topics": [
        "logLikelihoodMgev_UNI_inhom"
      ]
    },
    {
      "page": "logLikelihoodMgev_UNI_inhom_intCens",
      "title": "Loglikelihood of matrix-GEV using uniformization, when the intensity function is regressed on covariate informatino",
      "topics": [
        "logLikelihoodMgev_UNI_inhom_intCens"
      ]
    },
    {
      "page": "logLikelihoodMgev_UNI_intervalCensoring",
      "title": "Loglikelihood of matrix-GEV using uniformization",
      "topics": [
        "logLikelihoodMgev_UNI_intervalCensoring"
      ]
    },
    {
      "page": "logLikelihoodMgompertz_PADE",
      "title": "Loglikelihood of matrix-Gompertz using Pade",
      "topics": [
        "logLikelihoodMgompertz_PADE"
      ]
    },
    {
      "page": "logLikelihoodMgompertz_PADEs",
      "title": "Loglikelihood of PI with matrix-Gompertz using Pade",
      "topics": [
        "logLikelihoodMgompertz_PADEs"
      ]
    },
    {
      "page": "logLikelihoodMGompertz_RK",
      "title": "Loglikelihood of matrix-Gompertz using Runge-Kutta",
      "topics": [
        "logLikelihoodMgompertz_RK"
      ]
    },
    {
      "page": "logLikelihoodMgompertz_RKs",
      "title": "Loglikelihood of PI with matrix-Gompertz using Runge-Kutta",
      "topics": [
        "logLikelihoodMgompertz_RKs"
      ]
    },
    {
      "page": "logLikelihoodMgompertz_UNI",
      "title": "Loglikelihood of matrix-Gompertz using uniformization",
      "topics": [
        "logLikelihoodMgompertz_UNI"
      ]
    },
    {
      "page": "logLikelihoodMgompertz_UNI_inhom",
      "title": "Loglikelihood of matrix-Gompertz using uniformization, when the intensity function is regressed on covariate informatino",
      "topics": [
        "logLikelihoodMgompertz_UNI_inhom"
      ]
    },
    {
      "page": "logLikelihoodMgompertz_UNI_inhom_intCens",
      "title": "Loglikelihood of matrix-Gompertz using uniformization, when the intensity function is regressed on covariate informatino",
      "topics": [
        "logLikelihoodMgompertz_UNI_inhom_intCens"
      ]
    },
    {
      "page": "logLikelihoodMgompertz_UNI_intervalCensoring",
      "title": "Loglikelihood of matrix-Gompertz using uniformization",
      "topics": [
        "logLikelihoodMgompertz_UNI_intervalCensoring"
      ]
    },
    {
      "page": "logLikelihoodMgompertz_UNIs",
      "title": "Loglikelihood of PI with matrix-Gompertz using Uniformization",
      "topics": [
        "logLikelihoodMgompertz_UNIs"
      ]
    },
    {
      "page": "logLikelihoodMgompertz_UNIs_inhom",
      "title": "Loglikelihood of PI with matrix-Gompertz using uniformization, when the intensity function is regressed on covariate informatino",
      "topics": [
        "logLikelihoodMgompertz_UNIs_inhom"
      ]
    },
    {
      "page": "logLikelihoodMgompertz_UNIs_inhom_intCens",
      "title": "Loglikelihood of PI with matrix-Gompertz using uniformization, when the intensity function is regressed on covariate informatino",
      "topics": [
        "logLikelihoodMgompertz_UNIs_inhom_intCens"
      ]
    },
    {
      "page": "logLikelihoodMgompertz_UNIs_intervalCensoring",
      "title": "Loglikelihood of PI with matrix-Gompertz using Uniformization",
      "topics": [
        "logLikelihoodMgompertz_UNIs_intervalCensoring"
      ]
    },
    {
      "page": "logLikelihoodMloglogistic_PADE",
      "title": "Loglikelihood of matrix-loglogistic using Pade",
      "topics": [
        "logLikelihoodMloglogistic_PADE"
      ]
    },
    {
      "page": "logLikelihoodMloglogistic_PADEs",
      "title": "Loglikelihood of PI with matrix-loglogistic using Pade",
      "topics": [
        "logLikelihoodMloglogistic_PADEs"
      ]
    },
    {
      "page": "logLikelihoodMLogLogistic_RK",
      "title": "Loglikelihood of matrix-loglogistic using Runge-Kutta",
      "topics": [
        "logLikelihoodMloglogistic_RK"
      ]
    },
    {
      "page": "logLikelihoodMloglogistic_RKs",
      "title": "Loglikelihood of PI with matrix-loglogistic using Runge-Kutta",
      "topics": [
        "logLikelihoodMloglogistic_RKs"
      ]
    },
    {
      "page": "logLikelihoodMloglogistic_UNI",
      "title": "Loglikelihood of matrix-loglogistic using uniformization",
      "topics": [
        "logLikelihoodMloglogistic_UNI"
      ]
    },
    {
      "page": "logLikelihoodMloglogistic_UNI_inhom",
      "title": "Loglikelihood of matrix-loglogistic using uniformization, when the intensity function is regressed on covariate informatino",
      "topics": [
        "logLikelihoodMloglogistic_UNI_inhom"
      ]
    },
    {
      "page": "logLikelihoodMloglogistic_UNI_inhom_intCens",
      "title": "Loglikelihood of matrix-loglogistic using uniformization, when the intensity function is regressed on covariate informatino",
      "topics": [
        "logLikelihoodMloglogistic_UNI_inhom_intCens"
      ]
    },
    {
      "page": "logLikelihoodMloglogistic_UNI_intervalCensoring",
      "title": "Loglikelihood of matrix-loglogistic using uniformization",
      "topics": [
        "logLikelihoodMloglogistic_UNI_intervalCensoring"
      ]
    },
    {
      "page": "logLikelihoodMloglogistic_UNIs",
      "title": "Loglikelihood of PI with matrix-loglogistic using uniformization",
      "topics": [
        "logLikelihoodMloglogistic_UNIs"
      ]
    },
    {
      "page": "logLikelihoodMloglogistic_UNIs_inhom",
      "title": "Loglikelihood of PI with matrix-loglogistic using uniformization, when the intensity function is regressed on covariate informatino",
      "topics": [
        "logLikelihoodMloglogistic_UNIs_inhom"
      ]
    },
    {
      "page": "logLikelihoodMloglogistic_UNIs_inhom_intCens",
      "title": "Loglikelihood of PI with matrix-loglogistic using uniformization, when the intensity function is regressed on covariate informatino",
      "topics": [
        "logLikelihoodMloglogistic_UNIs_inhom_intCens"
      ]
    },
    {
      "page": "logLikelihoodMloglogistic_UNIs_intervalCensoring",
      "title": "Loglikelihood of PI with matrix-loglogistic using uniformization",
      "topics": [
        "logLikelihoodMloglogistic_UNIs_intervalCensoring"
      ]
    },
    {
      "page": "logLikelihoodMlognormal_PADE",
      "title": "Loglikelihood of matrix-lognormal using Pade",
      "topics": [
        "logLikelihoodMlognormal_PADE"
      ]
    },
    {
      "page": "logLikelihoodMlognormal_PADEs",
      "title": "Loglikelihood of PI with matrix-lognormal using Pade",
      "topics": [
        "logLikelihoodMlognormal_PADEs"
      ]
    },
    {
      "page": "logLikelihoodMLogNormal_RK",
      "title": "Loglikelihood of matrix-lognormal using Runge-Kutta",
      "topics": [
        "logLikelihoodMlognormal_RK"
      ]
    },
    {
      "page": "logLikelihoodMlognormal_RKs",
      "title": "Loglikelihood of PI matrix-lognormal using Runge-Kutta",
      "topics": [
        "logLikelihoodMlognormal_RKs"
      ]
    },
    {
      "page": "logLikelihoodMlognormal_UNI",
      "title": "Loglikelihood of matrix-lognormal using uniformization",
      "topics": [
        "logLikelihoodMlognormal_UNI"
      ]
    },
    {
      "page": "logLikelihoodMlognormal_UNI_inhom",
      "title": "Loglikelihood of matrix-lognormal using uniformization, when the intensity function is regressed on covariate informatino",
      "topics": [
        "logLikelihoodMlognormal_UNI_inhom"
      ]
    },
    {
      "page": "logLikelihoodMlognormal_UNI_inhom_intCens",
      "title": "Loglikelihood of matrix-lognormal using uniformization, when the intensity function is regressed on covariate informatino",
      "topics": [
        "logLikelihoodMlognormal_UNI_inhom_intCens"
      ]
    },
    {
      "page": "logLikelihoodMlognormal_UNI_intervalCensoring",
      "title": "Loglikelihood of matrix-lognormal using uniformization",
      "topics": [
        "logLikelihoodMlognormal_UNI_intervalCensoring"
      ]
    },
    {
      "page": "logLikelihoodMlognormal_UNIs",
      "title": "Loglikelihood of PI with matrix-lognormal using uniformization",
      "topics": [
        "logLikelihoodMlognormal_UNIs"
      ]
    },
    {
      "page": "logLikelihoodMlognormal_UNIs_inhom",
      "title": "Loglikelihood of PI with matrix-lognormal using uniformization, when the intensity function is regressed on covariate informatino",
      "topics": [
        "logLikelihoodMlognormal_UNIs_inhom"
      ]
    },
    {
      "page": "logLikelihoodMlognormal_UNIs_inhom_intCens",
      "title": "Loglikelihood of PI with matrix-lognormal using uniformization, when the intensity function is regressed on covariate informatino",
      "topics": [
        "logLikelihoodMlognormal_UNIs_inhom_intCens"
      ]
    },
    {
      "page": "logLikelihoodMlognormal_UNIs_intervalCensoring",
      "title": "Loglikelihood of PI with matrix-lognormal using uniformization",
      "topics": [
        "logLikelihoodMlognormal_UNIs_intervalCensoring"
      ]
    },
    {
      "page": "logLikelihoodMpareto_PADE",
      "title": "Loglikelihood of matrix-Pareto using Pade",
      "topics": [
        "logLikelihoodMpareto_PADE"
      ]
    },
    {
      "page": "logLikelihoodMpareto_PADEs",
      "title": "Loglikelihood of PI with matrix-Pareto using Pade",
      "topics": [
        "logLikelihoodMpareto_PADEs"
      ]
    },
    {
      "page": "logLikelihoodMPareto_RK",
      "title": "Loglikelihood of matrix-Pareto using Runge-Kutta",
      "topics": [
        "logLikelihoodMpareto_RK"
      ]
    },
    {
      "page": "logLikelihoodMpareto_RKs",
      "title": "Loglikelihood of PI with matrix-Pareto using Runge-Kutta",
      "topics": [
        "logLikelihoodMpareto_RKs"
      ]
    },
    {
      "page": "logLikelihoodMpareto_UNI",
      "title": "Loglikelihood of matrix-Pareto using uniformization",
      "topics": [
        "logLikelihoodMpareto_UNI"
      ]
    },
    {
      "page": "logLikelihoodMpareto_UNI_inhom",
      "title": "Loglikelihood of matrix-Pareto using uniformization, when the intensity function is regressed on covariate informatino",
      "topics": [
        "logLikelihoodMpareto_UNI_inhom"
      ]
    },
    {
      "page": "logLikelihoodMpareto_UNI_inhom_intCens",
      "title": "Loglikelihood of matrix-Pareto using uniformization, when the intensity function is regressed on covariate informatino",
      "topics": [
        "logLikelihoodMpareto_UNI_inhom_intCens"
      ]
    },
    {
      "page": "logLikelihoodMpareto_UNI_intervalCensoring",
      "title": "Loglikelihood of matrix-Pareto using uniformization",
      "topics": [
        "logLikelihoodMpareto_UNI_intervalCensoring"
      ]
    },
    {
      "page": "logLikelihoodMpareto_UNIs",
      "title": "Loglikelihood of PI with matrix-Pareto using uniformization",
      "topics": [
        "logLikelihoodMpareto_UNIs"
      ]
    },
    {
      "page": "logLikelihoodMpareto_UNIs_inhom",
      "title": "Loglikelihood of PI with matrix-Pareto using uniformization, when the intensity function is regressed on covariate informatino",
      "topics": [
        "logLikelihoodMpareto_UNIs_inhom"
      ]
    },
    {
      "page": "logLikelihoodMpareto_UNIs_inhom_intCens",
      "title": "Loglikelihood of PI with matrix-Pareto using uniformization, when the intensity function is regressed on covariate informatino",
      "topics": [
        "logLikelihoodMpareto_UNIs_inhom_intCens"
      ]
    },
    {
      "page": "logLikelihoodMpareto_UNIs_intervalCensoring",
      "title": "Loglikelihood of PI with matrix-Pareto using uniformization",
      "topics": [
        "logLikelihoodMpareto_UNIs_intervalCensoring"
      ]
    },
    {
      "page": "logLikelihoodMweibull_PADE",
      "title": "Loglikelihood of matrix-Weibull using Pade",
      "topics": [
        "logLikelihoodMweibull_PADE"
      ]
    },
    {
      "page": "logLikelihoodMweibull_PADEs",
      "title": "Loglikelihood of PI with matrix-Weibull using Pade",
      "topics": [
        "logLikelihoodMweibull_PADEs"
      ]
    },
    {
      "page": "logLikelihoodMWeibull_RK",
      "title": "Loglikelihood of matrix-Weibull using Runge-Kutta",
      "topics": [
        "logLikelihoodMweibull_RK"
      ]
    },
    {
      "page": "logLikelihoodMweibull_RKs",
      "title": "Loglikelihood of PI with matrix-Weibull using Runge-Kutta",
      "topics": [
        "logLikelihoodMweibull_RKs"
      ]
    },
    {
      "page": "logLikelihoodMweibull_UNI",
      "title": "Loglikelihood of matrix-Weibull using uniformization",
      "topics": [
        "logLikelihoodMweibull_UNI"
      ]
    },
    {
      "page": "logLikelihoodMweibull_UNI_inhom",
      "title": "Loglikelihood of matrix-Weibull using uniformization, when the intensity function is regressed on covariate informatino",
      "topics": [
        "logLikelihoodMweibull_UNI_inhom"
      ]
    },
    {
      "page": "logLikelihoodMweibull_UNI_inhom_intCens",
      "title": "Loglikelihood of matrix-Weibull using uniformization, when the intensity function is regressed on covariate informatino",
      "topics": [
        "logLikelihoodMweibull_UNI_inhom_intCens"
      ]
    },
    {
      "page": "logLikelihoodMweibull_UNI_intervalCensoring",
      "title": "Loglikelihood of matrix-Weibull using uniformization",
      "topics": [
        "logLikelihoodMweibull_UNI_intervalCensoring"
      ]
    },
    {
      "page": "logLikelihoodMweibull_UNIs",
      "title": "Loglikelihood of PI with matrix-Weibull using uniformization",
      "topics": [
        "logLikelihoodMweibull_UNIs"
      ]
    },
    {
      "page": "logLikelihoodMweibull_UNIs_inhom",
      "title": "Loglikelihood of PI with matrix-Weibull using uniformization, when the intensity function is regressed on covariate informatino",
      "topics": [
        "logLikelihoodMweibull_UNIs_inhom"
      ]
    },
    {
      "page": "logLikelihoodMweibull_UNIs_inhom_intCens",
      "title": "Loglikelihood of PI with matrix-Weibull using uniformization, when the intensity function is regressed on covariate informatino",
      "topics": [
        "logLikelihoodMweibull_UNIs_inhom_intCens"
      ]
    },
    {
      "page": "logLikelihoodMweibull_UNIs_intervalCensoring",
      "title": "Loglikelihood of PI with matrix-Weibull using uniformization",
      "topics": [
        "logLikelihoodMweibull_UNIs_intervalCensoring"
      ]
    },
    {
      "page": "logLikelihoodPH_MoE",
      "title": "Loglikelihood for PH-MoE",
      "topics": [
        "logLikelihoodPH_MoE"
      ]
    },
    {
      "page": "logLikelihoodPH_PADE",
      "title": "Loglikelihood of phase-type using Pade approximation",
      "topics": [
        "logLikelihoodPH_PADE"
      ]
    },
    {
      "page": "logLikelihoodPH_PADEs",
      "title": "Loglikelihood of PI with phase-type using Pade",
      "topics": [
        "logLikelihoodPH_PADEs"
      ]
    },
    {
      "page": "logLikelihoodPH_RK",
      "title": "Loglikelihood of phase-type using Runge-Kutta",
      "topics": [
        "logLikelihoodPH_RK"
      ]
    },
    {
      "page": "logLikelihoodPH_RKs",
      "title": "Loglikelihood of PI with phase-type using Runge-Kutta",
      "topics": [
        "logLikelihoodPH_RKs"
      ]
    },
    {
      "page": "logLikelihoodPH_UNI",
      "title": "Loglikelihood of phase-type using uniformization",
      "topics": [
        "logLikelihoodPH_UNI"
      ]
    },
    {
      "page": "logLikelihoodPH_UNI_intervalCensoring",
      "title": "Loglikelihood of phase-type using uniformization",
      "topics": [
        "logLikelihoodPH_UNI_intervalCensoring"
      ]
    },
    {
      "page": "logLikelihoodPH_UNIs",
      "title": "Loglikelihood of PI with phase-type using uniformization",
      "topics": [
        "logLikelihoodPH_UNIs"
      ]
    },
    {
      "page": "logLikelihoodPH_UNIs_intervalCensoring",
      "title": "Loglikelihood of PI with phase-type using uniformization",
      "topics": [
        "logLikelihoodPH_UNIs_intervalCensoring"
      ]
    },
    {
      "page": "LRT",
      "title": "New generic for likelihood ratio test between two matrix distribution models",
      "topics": [
        "LRT"
      ]
    },
    {
      "page": "LRT-ph-ph-method",
      "title": "LRT method for ph class",
      "topics": [
        "LRT,ph,ph-method"
      ]
    },
    {
      "page": "m_exp_sum",
      "title": "Computes exp(Sx) via series representation",
      "topics": [
        "m_exp_sum"
      ]
    },
    {
      "page": "marginal",
      "title": "New generic for the marginals of multivariate matrix distributions",
      "topics": [
        "marginal"
      ]
    },
    {
      "page": "marginal_expectation",
      "title": "Marginal conditional expectations",
      "topics": [
        "marginal_expectation"
      ]
    },
    {
      "page": "marginal-bivdph-method",
      "title": "Marginal method for bivdph class",
      "topics": [
        "marginal,bivdph-method"
      ]
    },
    {
      "page": "marginal-biviph-method",
      "title": "Marginal method for biviph class",
      "topics": [
        "marginal,biviph-method"
      ]
    },
    {
      "page": "marginal-bivph-method",
      "title": "Marginal method for bivph class",
      "topics": [
        "marginal,bivph-method"
      ]
    },
    {
      "page": "marginal-mdph-method",
      "title": "Marginal method for mdph class",
      "topics": [
        "marginal,mdph-method"
      ]
    },
    {
      "page": "marginal-miph-method",
      "title": "Marginal method for multivariate inhomogeneous phase-type distributions",
      "topics": [
        "marginal,miph-method"
      ]
    },
    {
      "page": "marginal-mph-method",
      "title": "Marginal method for multivariate phase-type distributions",
      "topics": [
        "marginal,mph-method"
      ]
    },
    {
      "page": "marginal-MPHstar-method",
      "title": "Marginal method for MPHstar class",
      "topics": [
        "marginal,MPHstar-method"
      ]
    },
    {
      "page": "matrix_exponential",
      "title": "Matrix exponential",
      "topics": [
        "matrix_exponential"
      ]
    },
    {
      "page": "matrix_inverse",
      "title": "Inverse of a matrix",
      "topics": [
        "matrix_inverse"
      ]
    },
    {
      "page": "matrix_power",
      "title": "Computes A^n",
      "topics": [
        "matrix_power"
      ]
    },
    {
      "page": "matrix_product",
      "title": "Product of two matrices",
      "topics": [
        "matrix_product"
      ]
    },
    {
      "page": "matrix_VanLoan",
      "title": "Creates the matrix (A1, B1 ; 0, A2)",
      "topics": [
        "matrix_vanloan"
      ]
    },
    {
      "page": "max_diagonal",
      "title": "Maximum diagonal element of a matrix",
      "topics": [
        "max_diagonal"
      ]
    },
    {
      "page": "maximum",
      "title": "New generic for maximum of two matrix distributions",
      "topics": [
        "maximum"
      ]
    },
    {
      "page": "maximum-dph-dph-method",
      "title": "Maximum method for discrete phase-type distributions",
      "topics": [
        "maximum,dph,dph-method"
      ]
    },
    {
      "page": "maximum-iph-iph-method",
      "title": "Maximum method for inhomogeneous phase-type distributions",
      "topics": [
        "maximum,iph,iph-method"
      ]
    },
    {
      "page": "maximum-ph-ph-method",
      "title": "Maximum method for phase-type distributions",
      "topics": [
        "maximum,ph,ph-method"
      ]
    },
    {
      "page": "mdph",
      "title": "Constructor function for multivariate discrete phase-type distributions",
      "topics": [
        "mdph"
      ]
    },
    {
      "page": "mdph-class",
      "title": "Multivariate discrete phase-type distributions",
      "topics": [
        "mdph-class"
      ]
    },
    {
      "page": "mdphdensity",
      "title": "Multivariate discrete phase-type density",
      "topics": [
        "mdphdensity"
      ]
    },
    {
      "page": "mean-bivdph-method",
      "title": "Mean method for bivdph class",
      "topics": [
        "mean,bivdph-method"
      ]
    },
    {
      "page": "mean-bivph-method",
      "title": "Mean Method for bivph class",
      "topics": [
        "mean,bivph-method"
      ]
    },
    {
      "page": "mean-dph-method",
      "title": "Mean method for discrete phase-type distributions",
      "topics": [
        "mean,dph-method"
      ]
    },
    {
      "page": "mean-mdph-method",
      "title": "Mean method for multivariate discrete phase-type distributions",
      "topics": [
        "mean,mdph-method"
      ]
    },
    {
      "page": "mean-mph-method",
      "title": "Mean method for multivariate phase-type distributions",
      "topics": [
        "mean,mph-method"
      ]
    },
    {
      "page": "mean-MPHstar-method",
      "title": "Mean method for MPHstar class",
      "topics": [
        "mean,MPHstar-method"
      ]
    },
    {
      "page": "mean-ph-method",
      "title": "Mean method for phase-type distributions",
      "topics": [
        "mean,ph-method"
      ]
    },
    {
      "page": "merge_matrices",
      "title": "Merges the matrices S11, S12 and S22 into a sub-intensity matrix",
      "topics": [
        "merge_matrices"
      ]
    },
    {
      "page": "merlang_dph",
      "title": "Mixture of Erlang (discrete) constructor",
      "topics": [
        "merlang_dph"
      ]
    },
    {
      "page": "merlang_ph",
      "title": "Mixture of Erlang (continuous) constructor",
      "topics": [
        "merlang_ph"
      ]
    },
    {
      "page": "mgevcdf",
      "title": "Matrix-GEV cdf",
      "topics": [
        "mgevcdf"
      ]
    },
    {
      "page": "mgevden",
      "title": "Matrix-GEV density",
      "topics": [
        "mgevden"
      ]
    },
    {
      "page": "mgf",
      "title": "New generic for mgf of matrix distributions",
      "topics": [
        "mgf"
      ]
    },
    {
      "page": "mgf-bivph-method",
      "title": "Mgf method for bivph class",
      "topics": [
        "mgf,bivph-method"
      ]
    },
    {
      "page": "mgf-mph-method",
      "title": "Mgf method for multivariate phase-type distributions",
      "topics": [
        "mgf,mph-method"
      ]
    },
    {
      "page": "mgf-ph-method",
      "title": "Mgf method for phase-type distributions",
      "topics": [
        "mgf,ph-method"
      ]
    },
    {
      "page": "mGompertzcdf",
      "title": "Matrix-Gompertz cdf",
      "topics": [
        "mgompertzcdf"
      ]
    },
    {
      "page": "mGompertzden",
      "title": "Matrix-Gompertz density",
      "topics": [
        "mgompertzden"
      ]
    },
    {
      "page": "minimum",
      "title": "New generic for minimum of two matrix distributions",
      "topics": [
        "minimum"
      ]
    },
    {
      "page": "minimum-dph-dph-method",
      "title": "Minimum method for discrete phase-type distributions",
      "topics": [
        "minimum,dph,dph-method"
      ]
    },
    {
      "page": "minimum-iph-iph-method",
      "title": "Minimum method for inhomogeneous phase-type distributions",
      "topics": [
        "minimum,iph,iph-method"
      ]
    },
    {
      "page": "minimum-ph-ph-method",
      "title": "Minimum method for phase-type distributions",
      "topics": [
        "minimum,ph,ph-method"
      ]
    },
    {
      "page": "miph",
      "title": "Constructor function for multivariate inhomogeneous phase-type distributions",
      "topics": [
        "miph"
      ]
    },
    {
      "page": "miph-class",
      "title": "Multivariate inhomogeneous phase-type distributions",
      "topics": [
        "miph-class"
      ]
    },
    {
      "page": "mixture",
      "title": "New generic for mixture of two matrix distributions",
      "topics": [
        "mixture"
      ]
    },
    {
      "page": "mixture-dph-dph-method",
      "title": "Mixture method for phase-type distributions",
      "topics": [
        "mixture,dph,dph-method"
      ]
    },
    {
      "page": "mixture-ph-ph-method",
      "title": "Mixture method for phase-type distributions",
      "topics": [
        "mixture,ph,ph-method"
      ]
    },
    {
      "page": "mLogLogisticcdf",
      "title": "Matrix-loglogistic cdf",
      "topics": [
        "mloglogisticcdf"
      ]
    },
    {
      "page": "mLogLogisticden",
      "title": "Matrix-loglogistic density",
      "topics": [
        "mloglogisticden"
      ]
    },
    {
      "page": "mLogNormalcdf",
      "title": "Matrix-lognormal cdf",
      "topics": [
        "mlognormalcdf"
      ]
    },
    {
      "page": "mLogNormalden",
      "title": "Matrix-lognormal density",
      "topics": [
        "mlognormalden"
      ]
    },
    {
      "page": "MoE",
      "title": "New generic for mixture-of-experts regression with matrix distributions",
      "topics": [
        "MoE"
      ]
    },
    {
      "page": "MoE-bivdph-method",
      "title": "MoE method for bivdph Class",
      "topics": [
        "MoE,bivdph-method"
      ]
    },
    {
      "page": "MoE-dph-method",
      "title": "MoE method for dph Class",
      "topics": [
        "MoE,dph-method"
      ]
    },
    {
      "page": "MoE-mdph-method",
      "title": "MoE method for mdph Class",
      "topics": [
        "MoE,mdph-method"
      ]
    },
    {
      "page": "MoE-mph-method",
      "title": "Fit method for mph/miph class, using mixture-of-experts regression",
      "topics": [
        "MoE,mph-method"
      ]
    },
    {
      "page": "MoE-ph-method",
      "title": "MoE method for ph Class",
      "topics": [
        "MoE,ph-method"
      ]
    },
    {
      "page": "moment",
      "title": "New generic for moments of matrix distributions",
      "topics": [
        "moment"
      ]
    },
    {
      "page": "moment-bivdph-method",
      "title": "Moment method for bivdph class",
      "topics": [
        "moment,bivdph-method"
      ]
    },
    {
      "page": "moment-bivph-method",
      "title": "Moment method for bivph class",
      "topics": [
        "moment,bivph-method"
      ]
    },
    {
      "page": "moment-dph-method",
      "title": "Moment method for discrete phase-type distributions",
      "topics": [
        "moment,dph-method"
      ]
    },
    {
      "page": "moment-mdph-method",
      "title": "Moment method for multivariate discrete phase-type distributions",
      "topics": [
        "moment,mdph-method"
      ]
    },
    {
      "page": "moment-mph-method",
      "title": "Moment method for multivariate phase-type distributions",
      "topics": [
        "moment,mph-method"
      ]
    },
    {
      "page": "moment-ph-method",
      "title": "Moment method for phase-type distributions",
      "topics": [
        "moment,ph-method"
      ]
    },
    {
      "page": "mParetocdf",
      "title": "Matrix-Pareto cdf",
      "topics": [
        "mparetocdf"
      ]
    },
    {
      "page": "mParetoden",
      "title": "Matrix-Pareto density",
      "topics": [
        "mparetoden"
      ]
    },
    {
      "page": "mph",
      "title": "Constructor function for multivariate phase-type distributions",
      "topics": [
        "mph"
      ]
    },
    {
      "page": "mph-class",
      "title": "Multivariate phase-type distributions",
      "topics": [
        "mph-class"
      ]
    },
    {
      "page": "MPHstar",
      "title": "Constructor function for multivariate phase-type distributions (MPH* class)",
      "topics": [
        "MPHstar"
      ]
    },
    {
      "page": "MPHstar_data_aggregation",
      "title": "Prepare data for the MPHstar_EMstep_UNI",
      "topics": [
        "MPHstar_data_aggregation"
      ]
    },
    {
      "page": "MPHstar_EMstep_UNI",
      "title": "EM step using Uniformization for MPHstar class",
      "topics": [
        "MPHstar_EMstep_UNI"
      ]
    },
    {
      "page": "MPHstar-class",
      "title": "Multivariate phase-type distributions obtained by transformation via rewards",
      "topics": [
        "MPHstar-class"
      ]
    },
    {
      "page": "mWeibullcdf",
      "title": "Matrix-Weibull cdf",
      "topics": [
        "mweibullcdf"
      ]
    },
    {
      "page": "mWeibullden",
      "title": "Matrix-Weibull density",
      "topics": [
        "mweibullden"
      ]
    },
    {
      "page": "n_pos",
      "title": "Find how many states have positive reward",
      "topics": [
        "n_pos"
      ]
    },
    {
      "page": "new_state",
      "title": "New state in a Markov jump process",
      "topics": [
        "new_state"
      ]
    },
    {
      "page": "Nfold",
      "title": "New generic for N-fold convolution of two matrix distributions",
      "topics": [
        "Nfold"
      ]
    },
    {
      "page": "Nfold-dph-method",
      "title": "Nfold method for phase-type distributions",
      "topics": [
        "Nfold,dph-method"
      ]
    },
    {
      "page": "pgf",
      "title": "New generic for pgf of matrix distributions",
      "topics": [
        "pgf"
      ]
    },
    {
      "page": "pgf-bivdph-method",
      "title": "Pgf method for bivariate discrete phase-type distributions",
      "topics": [
        "pgf,bivdph-method"
      ]
    },
    {
      "page": "pgf-dph-method",
      "title": "Pgf Method for discrete phase-type distributions",
      "topics": [
        "pgf,dph-method"
      ]
    },
    {
      "page": "pgf-mdph-method",
      "title": "Pgf method for multivariate discrete phase-type distributions",
      "topics": [
        "pgf,mdph-method"
      ]
    },
    {
      "page": "ph",
      "title": "Constructor function for phase-type distributions",
      "topics": [
        "ph"
      ]
    },
    {
      "page": "ph_laplace",
      "title": "Laplace transform of a phase-type distribution",
      "topics": [
        "ph_laplace"
      ]
    },
    {
      "page": "ph-class",
      "title": "Phase-type distributions",
      "topics": [
        "ph-class"
      ]
    },
    {
      "page": "phcdf",
      "title": "Phase-type cdf",
      "topics": [
        "phcdf"
      ]
    },
    {
      "page": "phdensity",
      "title": "Phase-type density",
      "topics": [
        "phdensity"
      ]
    },
    {
      "page": "plus_states",
      "title": "Find which states have positive reward",
      "topics": [
        "plus_states"
      ]
    },
    {
      "page": "pow2_matrix",
      "title": "Computes A^(2^n)",
      "topics": [
        "pow2_matrix"
      ]
    },
    {
      "page": "quan",
      "title": "New generic for the quantile of matrix distributions",
      "topics": [
        "quan"
      ]
    },
    {
      "page": "quan-ph-method",
      "title": "Quantile method for phase-type distributions",
      "topics": [
        "quan,ph-method"
      ]
    },
    {
      "page": "random_reward",
      "title": "Random reward matrix",
      "topics": [
        "random_reward"
      ]
    },
    {
      "page": "random_structure",
      "title": "Random structure of a phase-type",
      "topics": [
        "random_structure"
      ]
    },
    {
      "page": "random_structure_bivph",
      "title": "Random structure of a bivariate phase-type",
      "topics": [
        "random_structure_bivph"
      ]
    },
    {
      "page": "rcsph",
      "title": "Simulate common-shock phase-type",
      "topics": [
        "rcsph"
      ]
    },
    {
      "page": "rdphasetype",
      "title": "Simulate discrete phase-type",
      "topics": [
        "rdphasetype"
      ]
    },
    {
      "page": "reg",
      "title": "New generic for regression with matrix distributions",
      "topics": [
        "reg"
      ]
    },
    {
      "page": "reg-ph-method",
      "title": "Regression method for ph Class",
      "topics": [
        "reg,ph-method"
      ]
    },
    {
      "page": "revers_data_trans",
      "title": "Applies the inverse of the GEV transformation but giving back the resulting vector in reverse order",
      "topics": [
        "revers_data_trans"
      ]
    },
    {
      "page": "rew_sanity_check",
      "title": "Transform a reward matrix with very small rewards to avoid numerical problems",
      "topics": [
        "rew_sanity_check"
      ]
    },
    {
      "page": "riph",
      "title": "Random inhomogeneous phase-type",
      "topics": [
        "riph"
      ]
    },
    {
      "page": "rmatrixgev",
      "title": "Random matrix GEV",
      "topics": [
        "rmatrixgev"
      ]
    },
    {
      "page": "rMDPHstar",
      "title": "Simulate MDPH*",
      "topics": [
        "rMDPHstar"
      ]
    },
    {
      "page": "rMIPHstar",
      "title": "Simulate a MIPH* random vector",
      "topics": [
        "rMIPHstar"
      ]
    },
    {
      "page": "rMPHstar",
      "title": "Simulate a MPH* random vector",
      "topics": [
        "rMPHstar"
      ]
    },
    {
      "page": "rphasetype",
      "title": "Simulate phase-type",
      "topics": [
        "rphasetype"
      ]
    },
    {
      "page": "runge_kutta",
      "title": "Runge-Kutta for the calculation of the a and b vectors and the c matrix in a EM step",
      "topics": [
        "runge_kutta"
      ]
    },
    {
      "page": "show-bivdph-method",
      "title": "Show method for bivariate discrete phase-type distributions",
      "topics": [
        "show,bivdph-method"
      ]
    },
    {
      "page": "show-biviph-method",
      "title": "Show method for bivariate inhomogeneous phase-type distributions",
      "topics": [
        "show,biviph-method"
      ]
    },
    {
      "page": "show-bivph-method",
      "title": "Show method for bivariate phase-type distributions",
      "topics": [
        "show,bivph-method"
      ]
    },
    {
      "page": "show-dph-method",
      "title": "Show method for discrete phase-type distributions",
      "topics": [
        "show,dph-method"
      ]
    },
    {
      "page": "show-iph-method",
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